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Resource Sharing in the Edge: A Distributed Bargaining-Theoretic Approach

Faheem Zafari, Prithwish Basu, Kin K. Leung, Jian Li, Ananthram Swami, Don Towsley

TL;DR

Using synthetic and real-world data traces, it is shown numerically that the proposed NBS based framework not only enhances the ability to satisfy applications’ resource demands, but also improves utilities of different ESPs.

Abstract

The growing demand for edge computing resources, particularly due to increasing popularity of Internet of Things (IoT), and distributed machine/deep learning applications poses a significant challenge. On the one hand, certain edge service providers (ESPs) may not have sufficient resources to satisfy their applications according to the associated service-level agreements. On the other hand, some ESPs may have additional unused resources. In this paper, we propose a resource-sharing framework that allows different ESPs to optimally utilize their resources and improve the satisfaction level of applications subject to constraints such as communication cost for sharing resources across ESPs. Our framework considers that different ESPs have their own objectives for utilizing their resources, thus resulting in a multi-objective optimization problem. We present an $N$-person \emph{Nash Bargaining Solution} (NBS) for resource allocation and sharing among ESPs with \emph{Pareto} optimality guarantee. Furthermore, we propose a \emph{distributed}, primal-dual algorithm to obtain the NBS by proving that the strong-duality property holds for the resultant resource sharing optimization problem. Using synthetic and real-world data traces, we show numerically that the proposed NBS based framework not only enhances the ability to satisfy applications' resource demands, but also improves utilities of different ESPs.

Resource Sharing in the Edge: A Distributed Bargaining-Theoretic Approach

TL;DR

Using synthetic and real-world data traces, it is shown numerically that the proposed NBS based framework not only enhances the ability to satisfy applications’ resource demands, but also improves utilities of different ESPs.

Abstract

The growing demand for edge computing resources, particularly due to increasing popularity of Internet of Things (IoT), and distributed machine/deep learning applications poses a significant challenge. On the one hand, certain edge service providers (ESPs) may not have sufficient resources to satisfy their applications according to the associated service-level agreements. On the other hand, some ESPs may have additional unused resources. In this paper, we propose a resource-sharing framework that allows different ESPs to optimally utilize their resources and improve the satisfaction level of applications subject to constraints such as communication cost for sharing resources across ESPs. Our framework considers that different ESPs have their own objectives for utilizing their resources, thus resulting in a multi-objective optimization problem. We present an -person \emph{Nash Bargaining Solution} (NBS) for resource allocation and sharing among ESPs with \emph{Pareto} optimality guarantee. Furthermore, we propose a \emph{distributed}, primal-dual algorithm to obtain the NBS by proving that the strong-duality property holds for the resultant resource sharing optimization problem. Using synthetic and real-world data traces, we show numerically that the proposed NBS based framework not only enhances the ability to satisfy applications' resource demands, but also improves utilities of different ESPs.

Paper Structure

This paper contains 24 sections, 1 theorem, 23 equations, 7 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Methodology and contributions
  4. System Model
  5. Problem Formulation for Single Service Provider
  6. Multiple Service Providers Problem Formulation
  7. Assumptions
  8. Choice of utility function
  9. NBS for Resource Sharing among CSPs
  10. Primer on Nash Bargaining Solution (NBS)
  11. Proposed Framework
  12. Centralized NBS
  13. Distributed algorithm for NBS
  14. $j \in \mathcal{M}_n$:$\frac{\partial \mathcal{L}}{\partial x_{n,k}^{j}}=0$
  15. $l \in \{\mathcal{M}\backslash\mathcal{M}_n\}$: $\frac{\partial \mathcal{L}}{\partial x_{n,k}^{l}}=0$
  16. ...and 9 more sections

Key Result

Lemma 1

At the optimal solution, the optimal Lagrange multiplier vector corresponding to the capacity constraint is non-zero, i.e., $\boldsymbol{\alpha_k^{*}}>0$.

Figures (7)

  • Figure 1: Cooperation among ESPs
  • Figure 2: Utility, average request satisfaction and average resource utilization for Setting $1$ when SPs are working alone and using our proposed NBS framework.
  • Figure 3: Utility, average request satisfaction and average resource utilization for Setting $2$ when SPs are working alone and using our proposed NBS framework.
  • Figure 4: Utility, average request satisfaction and average resource utilization for Setting $4$ when SPs are working alone and using our proposed NBS framework.
  • Figure 5: Utility, average request satisfaction and average resource utilization for Setting $5$ when SPs are working alone and using our proposed NBS framework.
  • ...and 2 more figures

Theorems & Definitions (5)

  • proof
  • proof
  • Lemma 1
  • proof
  • proof